File Coverage

blib/lib/Math/NumSeq/GolayRudinShapiro.pm

Criterion	Covered	Total	%
statement	51	58	87.9
branch	5	6	83.3
condition	2	9	22.2
subroutine	14	17	82.3
pod	5	7	71.4
total	77	97	79.3

# Copyright 2010, 2011, 2012, 2013, 2014 Kevin Ryde

# This file is part of Math-NumSeq.
#
# Math-NumSeq is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by the
# Free Software Foundation; either version 3, or (at your option) any later
# version.
#
# Math-NumSeq is distributed in the hope that it will be useful, but
# WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
# or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
# for more details.
#
# You should have received a copy of the GNU General Public License along
# with Math-NumSeq.  If not, see .

package Math::NumSeq::GolayRudinShapiro;
use 5.004;
use strict;
use List::Util 'max','min';

use vars '$VERSION', '@ISA';
$VERSION = 71;

use Math::NumSeq;
use Math::NumSeq::Base::IterateIth;
@ISA = ('Math::NumSeq::Base::IterateIth',
        'Math::NumSeq');
*_is_infinite = \&Math::NumSeq::_is_infinite;

use Math::NumSeq::Repdigits;
*_digit_split_lowtohigh = \&Math::NumSeq::Repdigits::_digit_split_lowtohigh;

# uncomment this to run the ### lines
#use Smart::Comments;


# use constant name => Math::NumSeq::__('Golay-Rudin-Shapiro');
use constant default_i_start => 0;

use constant parameter_info_array =>
  [ {
     name    => 'values_type',
     share_key => 'values_type_1-101',
     type    => 'enum',
     default => '1,-1',
     choices => ['1,-1',
                 '0,1',
                ],
     # TRANSLATORS: "1,-1" offered for translation of the "," if that might look like a decimal point, otherwise can be left unchanged
     choices_display => [Math::NumSeq::__('1,-1'),
                         Math::NumSeq::__('0,1'),
                        ],
     description => Math::NumSeq::__('The values to give for even or odd parity.'),
    },
  ];

sub description {
  my ($self) = @_;
  my ($even,$odd) = (ref $self ? @{$self->{'values'}} : (1,-1));
  # ENHANCE-ME: use __x(), maybe
  return sprintf(Math::NumSeq::__('Golay/Rudin/Shapiro parity of adjacent 11 bit pairs, %s if even count %s if odd count.'),
                 $even, $odd);
}

sub characteristic_integer {
  my ($self) = @_;
  return (_is_integer($self->{'values_min'})
          && _is_integer($self->{'values_max'}));
}
sub characteristic_pn1 {
  my ($self) = @_;
  return ($self->{'values_min'} == -1 && $self->{'values_max'} == 1);
}

#------------------------------------------------------------------------------
# cf A022155 - positions of -1
#    A203463 - positions of +1
#    A014081 - count of 11 bit pairs
#    A020986 - cumulative 1,-1, always positive
#    A020990 - cumulative GRS(2n+1), flips sign at odd i
#    A020991 - position of last occurrence of n in the partial sums
#    A005943 - number of subwords length n
#
my %oeis_anum = ('1,-1' => 'A020985',  # 1 and -1
                 '0,1'  => 'A020987',  # 0 and 1
                 # OEIS-Catalogue: A020985
                 # OEIS-Catalogue: A020987 values_type=0,1
                );
sub oeis_anum {
  my ($self) = @_;
  return $oeis_anum{$self->{'values_type'}};
}

#------------------------------------------------------------------------------

sub new {
  my $self = shift->SUPER::new(@_);

  my @values = split /,/, $self->{'values_type'};
  $self->{'values'} = \@values;
  $self->{'values_min'} = min(@values);
  $self->{'values_max'} = max(@values);
  ### $self
  return $self;
}

# ENHANCE-ME: use as_bin() on BigInt when available
#
# ENHANCE-ME: use unpack() checksum 1-bit count as described by
# perlfunc.pod, if fit a UV or C "int" or whatever
#
#     # N & Nshift leaves bits with a 1 below them, then parity of bit count
#     $i &= ($i >> 1);
#     return (1 & unpack('%32b*', pack('I', $i)));
#
sub ith {
  my ($self, $i) = @_;
  if ($i < 0) {
    return undef;
  }
  if (_is_infinite($i)) {
    return $i;
  }

  my $prev = 0;
  my $xor = 0;
  foreach my $bit (_digit_split_lowtohigh($i,2)) {
    $xor ^= ($prev & $bit);
    $prev = $bit;
  }
  return $self->{'values'}->[$xor];
}

sub pred {
  my ($self, $value) = @_;
  return ($value == $self->{'values'}->[0]
          || $value == $self->{'values'}->[1]);
}

# Jorg Arndt fxtbook next step by
# low 1s 0111 increment to become 1000
# if even number of 1s then that's a "11" parity change
# and if the 1000 has a 1 above it then that's a parity change too
# so flip if 10..00 is an odd bit position XOR the bit above it


#------------------------------------------------------------------------------
sub _is_integer {
  my ($n) = @_;
  return ($n == int($n));
}

1;
__END__